Any DNA evidence allegedly found in the back of a car hired by Kate and Gerry McCann can easily be explained in an innocent way, family sources said yesterday, and is likely to prove "totally useless" in building a case against them.

In the first detailed rebuttal of accusations that Mr and Mrs McCann were involved in their daughter, Madeleine's, disappearance, a source close to the couple said yesterday there were "entirely innocent reasons" why her DNA may have been found in the car which could demolish the police case against them.

Leaks emerging from the police inquiry into the child's disappearance on May 3 have suggested that Portuguese investigators have uncovered traces of Madeleine in the Renault Scenic which her parents rented 25 days after she vanished. This evidence has formed the basis of the police case against the couple, which led them to name them as formal suspects in her disappearance 12 days ago.

But in briefings to journalists yesterday, the source said at least 30 friends and family members had used the car before police tested it, several of them blood relatives, and the car had also been used to transport Madeleine's belongings when the family moved holiday apartments.

The source said experts had told the family that DNA on some of these items, such as sweat on her sandals, could account for the traces allegedly found by police. Until now the family have declined to release details of their defence, citing Portugal's strict secrecy laws.

"People need to consider what was carried in that car for entirely innocent reasons," the source said. "When viewed as a whole by any rational person these reasons at best raise fundamental questions about the reliability of any so-called evidence and at worst render it totally useless."

The intervention came as Mr and Mrs McCann's new spokesman defended the couple against the "ludicrous" suggestion that they were involved in Madeleine's disappearance. Clarence Mitchell, a former BBC reporter and civil servant, said the couple were "the innocent victims of a heinous crime", adding the suggestion they had harmed their daughter was "as ludicrous as it is nonsensical".

Yesterday's developments signalled a proactive strategy in the couple's campaign to find their daughter and assert their innocence, and followed meetings with their lawyers. The couple have been subject to press speculation over their possible guilt and a swelling tide of public hostility. A newspaper opinion poll on Sunday found that only 20% of Britons believe they are completely innocent.

Mr Mitchell, who assisted the McCanns in May and June while acting on behalf of the Foreign Office, said he was so convinced of their innocence that he had given up his government career to help them.

A Portuguese judge is reviewing police evidence against the couple, and must decide this week whether to act. But local newspapers have reported that Judge Pedro Daniel dos Anjos Frias has denied Portuguese investigators permission to summon Mrs McCann back to Portugal for further questioning.

In their first interview since returning home to Britain Mr and Mrs McCann said they talk to their two-year-old twins about their missing sister "all the time".

They said when they ask where their older sister is they reply: "She isn't here at the moment."